Question

Imagine an economy with production function Y = F(K) = and 400 units of capital. If the depreciation rate is δ = .05, how much capital will deteriorate in the next period?

Answer 1

To find the equilibrium output for this economy, the national income (Y) is set equal to aggregate expenditure (AE), and all given economic components are considered. When solving for the equilibrium with a potential GDP of 3,500, one can either solve for G directly or calculate the multiplier to determine the change in G needed for achieving the desired level.

Step-by-step explanation:

To find the equilibrium level of output for the economy given in the question, we start by setting up the aggregate expenditure (AE) equation with the given components:

AE = C + I + G + X - M

Where:

• C = Consumption = 400 + 0.85(Y - T)
• I = Investment = 300
• G = Government spending = 200
• X = Exports = 500
• M = Imports = 0.1(Y-T)
• T = Taxes = 0.25Y

Equilibrium is when AE = Y (National Income).

At potential GDP of 3,500, to find the new level of G required, we substitute Y with 3,500 and solve for G:

3500 = 400 + 0.85(3500 - 0.25 × 3500) + 300 + G + 500 - 0.1(3500 - 0.25 × 3500)

To calculate the multiplier, we use the formula 1/(1-MPC(1-T)):

MPC (marginal propensity to consume) = 0.85 and T (tax rate) = 0.25. Substitute these values into the multiplier formula to find the multiplier effect on the national income, which can then be used to solve for the change in G that will achieve the desired increase in Y.